Puzzle



June 5, 1923. 1,457,383

W. H; MILLER PUZZLE Filed Aug. 18 1920 '7 Sheets-Sheet l WEMZZe f /fiz y June 5, I923.

w. H. MILLER PUZZLE Filed Aug. 18 1920 '7 Sheets-Sheet 3 I [fire/1 far WEMZ/er viii;

June 5, 1923.

W. H. MILLER PUZZLE Filed Aug. 18 1920 7 Sheets-Sheet 4 [7 2 V6112 0/" WHM/ZBI June 5, 19211- 1,457,383

' w. ,H. MILLER PUZZLE Filed AuK. l8 1920 7 Sheets-Sheet 5 /4 WHZZZ'ZZW 9? 7f By. I "Ji l? June 5, 1923.

W. H. MILLER PUZZLE Filed Auz. 18, 1920 7 sheets sheet 6 Patented June 5, 1923. d i

M T -ED jsr a rs {PATENT WILLIAM MILLER, OFI-IILLSBORO, ILLINOIS.

- PUZZLE.

* lkpplicationlffiled Aug11st.i18,-, 1,920. Serial, No. 404 .401.

To all'wkom it-mag i-co ncem Figures 13,114 l5 'sho w' modified ar- Be it-known that'I, WILIJAM-HI-MILLE a rangements of ,said key. r

eiti'zen'of the United States; and residing at Figures 16,17, 18 vnd l9 r ShOW anQ the' r Hillsboro, Illinois,-have invented the new embodiment. v V 5 and useful 'Improvernent inflPu zzles, of Referring now "to; the accompanying X'vhi'eh the following-isa specification; drawings, 10 designates a box or container This invention relates to puZz-les' having in which the puzzle-niay, bel p'ack edi particular reference to -number i'puz'zles stored. The puzzle proper comprises a .puz-

wherein the solution ofthe'puzzledepends zle board 12 which nay be of Wood, .card 0 upon certain arrangements of numbers. board, orhany other, suitablenaterial and One of the objects ofth'is'invention is to which maybe p ovided, ith perforations provide a puzzle'which is more or less'd-i-ffior sojeke'ts 'l3, adapted to receive and retain cult of soluti on,-"whichshallliold'the-interest number plugs 1 L. Each of theplugg may 00 of' theone attemptingtosolve it and which have anumber printed, Written or otherwise 15 shall be capable of considerable variation. impressed thereon or some oflthemmay be Further objects will appear 'fronrthe deleft blank. These plugs maybe constructed tail description taken in connection with to fitfthe sockets 'l 3,'so t hat when inserted the a'c'company-ingdraudng'inwhich: therein, they. Willjb'e. frictionallyi retained F igure 1' shows a top view oft-he puzzle All o-fthe plugs may be loose or removable 20 board with the number plugs rem-oyed; from the board 12, or some may be fixed and Figure 2 shows' the puzz'le board with the some lo'osefi. The'so'ckets 13 are preferably number plugs in place to'show one solution arranged in a rectangular pattern, that i's ofthe puzzle; so as, to form vertical rows'of numbersA Figure 3 showss'ixteen' different cover B,"C-; D, andhorizontal rows-Q F,' G,' H 25 cards forthis uzzle; v although this. arrangement is no-tessential, Figure 'showsoneof the'covereards apas numerous other'patt'erns maygbe'worked' pliedt'o' the puzzle'board; out; Y

Figure 5 shows the same eovercardcap- 'The numerals '16't0 31 inelusive designate pliedt'o the samepu'zzle board in a 'difi.'erent cover'carcls which may be-of paper, 'eard 30 position. I board or any other suitable niateriah'pr'efen Figure '6 showsthe same cover cardapably of the same sizeandlshape as the p'uz plied to the same puzzle bo'ard but in inzleflboard 12, though this is. notessential,

verted position from that of Figure 4; and adapted to" be, superimposed; thereon so Figure 7 sho-ws ithe same cover Lcard apas gi e e w fi E h cover card plied to the same puzzleiboard in" inverted has a seriesoflperforations 1,. 2f; 3,-fand 4; position from.that'shown.inl'Figure 5;; h p t n ing s1tuatedjthatwhen Figure 8 showsthe' arrangement-of the the r ca d i gl tl with t e. pu l puzzle board and the cover wcards packed in rd,- One 'Of-theplugs Will fil li da"containe r; V 'l lQ gh "said: perforation in the-"cover card: 40 Figure 9 shows a'puzzleb'oard of m'odi The =pe i Qns' and 4may be arfied'construction; rangedin a'numberrofdifferent patterns I Figure 10 shows a; partial section taken as shown in F 1g'ure'3 and the solution of the on line10 10"of.Figure"9;- puzzle consists in-so arranging the number F igure 1'1 sho'wsa number plug removed plugs 14- in the: puzzle board IQ thatxWhen 45 from-the board"; I p any'oi the cardslfi; to; 31;;1nc-lus1 vissu-pe're Figure il show's a key fofi the puzzle; imposed on sa1d-b0ard;thesum ofthe num= J nd v bers disclosed; through" thepe -io anons 2,'

3 and 4, will be the same in whatever posi tion the cover card is placed in proper registry with the board. Any of the cards shown in Figure 3 may be placed upon the board shown in Figure 2 in any position and either side up, and the sum of the numbers disclosed through the perforations will always he the same, namely 34 in the present case. This is clearly shown in Figures l, 5, 6 and 7 in which the card 17 is shown placed upon the board shown in Figure 2 in four out of a possible eight positions. lVhile only four positions are shown, all eight positions will give the same result.

Figures 9 and 10 show a slightly modified construction of the puzzle board 12. In this construction the puzzle board 32 consists of two sheets of card board or other suitable material mounted one upon the other, the upper sheet having perforations 33' adapted to receive the number plugs 14, and the lower sheet having somewhat smaller perforations 34 arranged to register with the pen forations 33 of the upper sheet so as to form a shoulder 35 adapted to support the plug 14:. The hole 3a allows for the insertion of the finger, to remove the plug.

The arrangement of numbers shown in Figure 2 is, of course, not the only arrangement that can be used for a puzzle according to this invention. Numerous other arrange ments are available. Such arrangements are in fact so numerous that it is convenient to havea key whereby a new number set may be obtained at any time. Such a key is shown in Figures 12 to 15 inclusive. This key comprises a board similar to the puzzle board which may be provided with a set of symbols in place of numbers arranged in a pattern similar to that of the puzzle board. In the present instance, the letters of the alphabet have been used as syinbols. This board may be sub-divided into a number of sections, in the present instance, four quarter sections 10 to 43 inclusive. The quarter sections may be provided with finger notches 4:4 for convenience in manipulation.

It willbe seen that the letters in Figure 12 taken in alphabetical order are arranged 1 in the same pattern as the numbers in Figure 2 taken in numerical order. In other words, by substituting, in Figure 2, A for 1, B for 2, C for 3, etc, in alphabetical and numerical order respectively, the arrange ment of Figure 12 is obtained. The arrangement of Figure 2 can .be obtained from the arrangement of Figure 12 by reversing this process. Similarly, by substituting in Figure 12 any other set of consecutive numbers, maintaining, of course, the correspondence of alphabetical and numerical order as pointed out above, a new number set will be obtained, which will fulfill the requirements of this invention as pointed out above. The numbers substituted need not, however, be in consecutive numerical order, but number sets may be obtained by a process to be described hereinaftr-ir, which when applied to the key shown in Figures 12 to 15 inclusive, or any of the other keys to be described hereinafter, will produce a number pattern which will fulfill the requirements of'this puzzle.

With any given number set applied to the key of Figure 12, a number of different number patterns may be obtained by manipulation of said key. If each of the quarter sections blocks 40, 41, 12 and 43 is rotated in dividually in the same direction through ninety degrees from its position in Figure 12, as indicated by the arrows in that figure, a second pattern will be obtained as shown in Figure 13. This pattern will also fulfill the requirements of the puzzle. This operation may be repeated and after rotation will produce a new pattern. The fourth pattern so found is shown in Figure 14.

If the above rotation be again performed on Figure 14, the original pattern of Figure 12 will be obtained. If, however, instead of repeating said rotation, the two lower blocks of Figure 14 be transposed so as to lie above the two upper blocks as indicated by the arrows in that figure, a new pattern will be ob tained as shown in Figure 15. (The two right hand blocks may be interchanged with the left hand blocks just as well.) Starting with the arrangement of Figure 15, the rotation process can again be performed three times, obtaining a new pattern each time. Thus from the key of Figure 12, a total of eight different patterns may be obtained.

If we start with other patterns than those shown in Figure 12 by using the same set of symbols, still other number patterns may be obtained from the same number set, which willfulfill the requirementsof the puzzle. A number of key patterns which may be used are shown in the following tabulation in which the letters given in the first line correspond to those of figure 12 and each succeeding line gives a new pattern which may be applied to the key by substituting each letter in that line for the letter above it in column in the first line.

From each of these, eight patterns maybe obtained by the rotation process described above. It will be seen that by this process a large number of different number patterns may be obtained from the same number set.

An enormous number of different number sets may be obtained which when applied to th key described above will fulfill the con ditions of the puzzle. A method of obtaining such number sets is illustrated in the following tabulation. In the first line are. the let.- ters or other symbols cerresponding t the key of Figure 12- Each succeeding line repres n a w num r set h h may be an:

' plied to the key substituting eachnumber in 1 1 that setf rthel t er a ov it i ol m A eonnnenie KLMNQ (X) (W) (X) (Y) (XHW) (X) 012 (W). 1 2 3. 4 5 6 7 .8. 9101112 131 11516 -9 s -.7 T6 -.5 1. +2 :=2.1. o ...1 2- e 4- 5- 14 13 6 5-10 Q 2 1.16 8' 7 1 2 11w/l. 3.. .3 2 1 -O 13 14 .15 '16 16 17. 18 19 32' 33 34 35 The letters EX, Y and Z placed between successive terms of the -a hoye series of numbers represent the algebra o'dlfi'erence between successiveterms. Wherever the Same letter appears, said difference must be th same. These differences may have any value,

but such value must always be the same for the same letter during aSer-ies. Thus,

In the first series 1 "W: 1 X: 1 :Y: 1 '1 Z: 1

In the second se es W: 1 X: '1 Y: 1 Z: 0

In the third series X:1 Y: 5 'Z::15

In the fourth series W 1 X741 Y p es o t d r mh pa tern; 9 eert in numbers may be permanently located in the pattern and one or more solutions required.

The following is, .41 illustration of. two solutions which-may be obtained with the numbe eteons stng of the numbers t 16, in which-.thewn-umber 8 has been vomitted from the pattern, and thenumbersi 1 3, 1.6

and the blank have been fixed in the pattern.

1a .6 15 10 3.4 1215's, 71am 11 1.1 1 1e 5 2 9 1e V will beinoted that in the second and. I

fourth series of numbers given above, one of the numbers is zero. This, of course, is

the same as if 110 number at all were given,

or a blank space left on the board.- This means that when the puzzle is presented for solution the .zero may be replaced by some arbitrary number which will prevent asuc cessful solution. until'discarde'd. In suchacase, of course, instructionsshould begiven to discard, or replace one number. It [will be obvious also that any other number than zero can be treated in the same way.

Various modifications of this puzzle are possible. For instance, two or more puzzle boards may be. combined. 'When four are combined making onepuzzleboard consisting of four boardsas described above, in

the form of a square, cover cards can be provided havingtheir perforations arranged as combinations of the arrangements shown .inFigure 3, so that they may be applied to the puzzle board: in -any position with a similar result as obtained with the single board. v

A way of combining four puzzle boards in such a way to make the puzzle'more difiicult of solutiomisshown in Figures l6'to 19.

Figure 16 represents a puzzle board having in all SlXtYrfOUI- spaces for numbers, ar-- ranged in a square with eight spaces on each side; For the sake of olearness in nomenclature, we may consider this board asdivided into, four quadrants, each .quadrantflbeing divided into four quarter sections and each quarter, section into four spaces? The quarter sect ons'of this board arelettered,

each at its center, with letters placed to cor re -p nd w h a puzz e board. e lla teen numhepspa'ces as describedfabove,

Each of the quarter sections of the presb eor ep nds t e ingl um space of'thesixteen space board, asipreviously described, and the letters are, placed on said sections according to-the original key pat-tern, as describedfor such aboard.

The spaces of each quarter section are lettered with the same letters as applied to that section and in addition, are numbered to indicate their relative positions in that quarter section. Thus, the quarter section A, has four spaces A 1, A 2, A 3, and A l, and similarly for all the other quarter sections. The numbering of the spaces of each quarter section maybe determined as follows:

First, each space is given a letter corresponding to the letter of its quarter section. Next, a pattern is selected such as shown in Figure '17, which may be superimposed upon one quadrant of the board so as to discloseone space of each quarter section of that quadrant. In each space so disclosed, the number 1 is added to the symbol for that space, so that, for instance, the first spaces of the first quadrant will bear the symbols A 1, N 1, K 1, and H 1. The pattern may now be turned about the vertical center line of the board as an axis, (Figure 19) so as to lie upon the second quadrant of the board. It will now disclose one space of each quarter section as before. The spaces so disclosed are numbered'l, as before. The pattern may now be turned about the horizontal center line of the board as an axis so as to lie upon the third quadrant, and again the spaces disclosed are each numbered 1. The process is again repeated by turning the pattern about the vertical center line as an axis so as to lie upon the fourth quadrant, and the disclosed spaces are again numbered 1.

We now have sixteen spaces bearing symbols A 1, B 1, C- 1, etc., up to P l, and located in quarter sections arranged relatively to each other to correspond with the original key pattern. These numbered sections are furthermore located symmetrically with respectto the center of the board.

If the pattern is now turned about the horizontal center line of the board as an axis from its last position in the fourth quadrant. it will regain its first position in the first quadrant. The pattern may now be rotated about an axis through its center and perpendicular to the plane of the paper to a new position over the first quadrant and a new set of four spaces will be disclosed. These four spaces may now be numbered 2, so as to complete the symbols A 2, N 2, K 2 and H 2. The process of rotating the pattern successively about each of the center lines of the board, as described before, may now be repeated so as to complete the symbols of a second set of spaces A 2, B 2, C 2, etc., up to P. 2. we now have a second set of symbols placed in the quarter sections according to the ori inal key pattern.

By continuing this process, proper symbols maybe placed. in all of the spaces of the board, and we will have four'completc sets of symbols, each arranged on the board in the quarter sections according to the original key pattern. The pattern used in producing this arrangement may be varied by omitting some of the perforations, or shifting their location, provided that by so doing, no space in a quadrant is disclosed inmore than one position of the pattern.

The pattern shown in Figure 16 may be varied by rotating all of the quarter sections as described for Figures 12 to 15 inclusive. The numbers to be applied to the spaces are obtained by taking any four number sets, obtained as previously described, and applying one to each of the symbol sets A 1',B 1, etc., A. 2, B 2, etc., A 3, B 3, etc., A 4, B 4, etc.- Such number sets must, however, have the same values of W, X, Y and Z and in addition, the difference between P 1 and A 2 must be equal to the difference between P 3 and A a.

It will be seen that apuzzle is, therefore, produced which, when certain numbers are left out, will be very diilicult of solution.

Another type of cover card (Fig. 19) may be produced by arranging the perforations so as to disclose numbers similarly located in each of the four quadrants. By this is meant, an arrangement which would dis close, for instance, 1, 2 or 3 adjacent numbers in the upper left hand corner of each quadrant.

It is obvious that various changes may be made in the details of construction with out departing from the spirit of this invention; it is, therefore, to be understood that this invention is not to be limited. to the specific details shown and described.

Having thus described this invention, what is claimed is:

1. A puzzle comprising a set of numbers to be arranged in a pattern, and a second fixed pattern adapted for superposition thereon and individually defining certain number locations such that an arithmetical operation performed upon the numbers common to both patterns will yield a constant result irrespective of the relative positions of said patterns.

2. A puzzle comprising a set of numbers to be arranged in a main pattern, and a plurality of auxiliary patterns adapted for superposition thereon and each individually defining certain number locations, such that an arithmetical operation performed upon the numbers common to said main pattern and any of said auxiliary patterns will yield a constant result for all of said auxiliary patterns.

3. A puzzle comprising a set of numbers to be arranged in'a main pattern, and a plurality of auxiliary patterns adapted for superposition thereon and each individually defining certain number locations, such that an arithmetical operation performed upon the numbers common to said main pattern and, any of said auxiliary patterns will yield a constant result for all of said auxiliary patterns, and for any relative position 'of said main and auxiliary patterns.

4;. Apuzzle comprising aset of numbers to, be arranged in a plurality of patterns,

and a second fixed pattern adapted for superposition on any of; said first patterns so. as to individually define certainnumberlocations, such that an arithmetical operation performed on the ,numbersfcommon to both patterns Willyield a constant result for all of said first patterns.

5. A puzzle comprising a set of numbers to be arranged in a plurality of patterns, and a second fixed pattern adapted for, super-position on any of said first patterns so as to individually define certain, number locations, such that an arithmetical operationperformed on the numbers common to both patterns will yield a :constant result for all of said first patterns irrespective of the relative second patterns.

6. A puzzle comprising a set .of numbers to be arranged in a plurality of patterns, a plurality of second patterns adapted for super-positionv on saidfirst patterns and each individually defining certain number locations, such that an arithmetical operation performed on the numbers common to any of'said first patternsand' any of said second patterns'wvi ll yield a constant result.

7. A puzzle comprisinga set of numbers to be arranged in a plurality of patterns. a plurality of second patterns adapted for super-position on said :first patterns-and each individually defining certain number locations, such-that an arithmetical ope-ration performed on the numbers common to any of said first patterns and any of said second patterns will yield a constant result irrespective of the relative positions of said first and second patterns. a 2..

. 2 '8. -A puzzle oom-prising a setgof numbers to be arranged in a'pattern, and a second pattern adapted for super-position thereon; such that an arithmetical operation pe'rformed onthe numbers "common to both patterns will yield a constant result irrespective of the relative positions of said patterns, said fi'rst pattern being'such that one or more of'sai'd numbers may be discarded and the remaining. numbers. 'rearranged into a new: pattern which will satisfy thesame --requirements. P y I 9. A puzzlecomprising' aset' of numbers tubearran ed in a. main pattern, and a pinrality of auxiliary patterns adapted for superposition thereon, such that an arithanetical operation performed upon the numbers temmon to said main pattern and any of said auxiliary atternswilliyie'ld acouivill satisfy the same requirements.-

positions of said first and stant result for all of said auxiliary patterns, said main pattern, being such that" one or more of saidnumbers may be discarded and thegremaining: numbers rears, 'rangedinto a new pattern which will satisfy; the same requirements.

-10. Apuzzle-comprising aset of numbers 7 to be arranged in a main pattern, and .aplurality of auxiliary patterns adapted for super-position thereon, such that an arithq meticaloperation performed upon the num bers common to saidmain pattern and any ofsaid auxiliary patterns will yield a con-- stant resu-ltforall ofsaid auxiliary patterns" and for any relative position .of saidv main and. auxiliary patterns, said main pattern may be discarded and the'remaining num-J bers rearranged into anew pattern which 11. A puzzle comprising a set of numbers to be arranged ins plurality :of patterns,and a second pattern adapted for super-position on any of said first-patterns, such tha't an arithmetical operation performed on the numbers common to both patterns will yield a, constant result-for all of said first patterns said first. patterns reach being-such that tone or: more of: said numbers may be discarded and the; remaining numbers rearranged into. a new. pattern which will satisfy the same lrequlrements. v

12. A puzzlecomprising a setlofinumbers' to .bev arranged in a plurality. of patterns,

and a second pattern adaptedforsupen' position on any of said first patterns,such that an arithmetical operati'onperformed on the numbers common to both-patterns will yield a constant result foral lffof said first:- patterns irrespective of the relativew'positions ofv said first and second patterns said main pattern being such;thatpne oryinor e of said numbers may be. discarded and the remaining. numbers rearranged into a a new pattern Which will satisfythe same requirements. I 13. A puzzle, comprising a set of numbers to be arrangedin apluralityofkpattennsyfl I plurality of second pat-terns adapted for super-position on said-"first patterns, such that an arithmeticaloperation performed on the numbers common to any of said first" patterns and any of said second-patterns will yield a constant result, said first patterns each ,beingsuch that {one or more of said numbers may be discarded and the aremaining numbers. rearranged into a new pattern :which will satisfy the sameirequire -ments..; 14.:A puzzle comprising a set of numbers to "be arrangedin a' plurality *ofwpatterns a pluralityrof second pat-terns adapted fo'r super-position on said first patt-erns such. that an arithmetical operation performed on the numbers ICOIIlIflOIIitO .any of ,-;said first patterns and any of said second patterns will yield a constant result, irrespective of the relative positions of said first and second patterns said first patterns each being such that one or more of said numbers may be discarded and the remaining numbers rearranged into a new pattern which will satisfy the same requirements.

' 15. A puzzle comprising a set of numbers tobe arranged in a pattern, and a second pattern adapted for superposition thereon, said first pattern being such that one or more of said numbers may be discarded and thereafter an arithmetical operation performed on the numbers common to both said superposed patterns will yield a constant re;

sult irrespective of the relative positions of said pattern. I

16. A puzzle comprising a set of numbers to be arranged in a pattern, and a second pattern adapted for superposition thereon, said firstpattern being such that one or more of said numbers may be replaced by another number and thereafter an arithmetical operation performed on the number common to both said superposed patterns will yield a constant result irrespective of the relative positions of said patterns.

17. A key for a number puzzle, comprising, a set of symbols arranged in a pattern adapted for finding number sets for the puzzle by substitution of numbers for said symbols, said pattern being arranged in subdivisions adapted by rearrangement to form new number sets.

18. A key for a number puzzle, comprising, a set of blocks each having a-set of symbols and adapted for juxtaposition to form a pattern wherefrom a number set may be obtained by substitution of numbers for said symbols, and means for rearranging said blocks to form new number sets.

' 19. A puzzle comprising a set of numbers to be arranged in a pattern, and a second pattern adapted for super-position thereon such that an arithmetical operationv performed uponthe numbers common to both patterns will yield a constant result irrespective ofthe relative positions of said patterns, said first v pattern being adapted to have certain of its numbers fixed in relative position therein, and the rest rearranged to form a new pattern adapted to fulfill the same requirements.

20. A puzzle comprising a set of numbers to be arranged in a main pattern, and a plurality of auxiliary patterns adapted for super-position thereon, such that an arithmetical operation performed upon the numbers common to said main pattern and any of said auxiliary patterns will yield a constant result for all of said auxiliary patterns, said vmain pattern being adapted to have certain of its numbers fixed in relative position therein, and the rest rearranged to form a adapted to have certain of its numbers fixed in relative position therein, and the rest rearranged to form a new pattern adapted to fulfill the same requirements.

22. Apuzzle comprisinga plurality of numbered members, means for supporting said numbered members, and perforated members adapted for engagement over said numbered members to disclose certain of said numbered members to produce when added together a predetermined sum regardless of the position of the perforated members upon said numbered members. i

23. A puzzle comprising a supporting member, numbered members adapted for various arrangements upon said supporting member, andperforated sheets adapted for engagement over said numbered members to disclose certain of said numbered members to produce a predetermined sum When added together regardless of the position of the perforated sheets.

24 A puzzle comprising a supporting member, perforated discs adapted for arrangement upon said supporting member, and reversible perforated sheets adapted for engagement over the numbered discs to disclose certain of said discs for producing when adding together a total predetermined sum when said perforated sheets are in various positions upon said numbered discs.

25. A puzzle comprising a supporting member, a set of numbered discs adapted for various arrangements upon said supporting member, and numbered sheets adapted for engagement in various positions upon said perforated discs when the latter are in their different arrangements to disclose certainof said discs to produce a predetermined sum when the numbers on the discs are added together, the same total sum being produced by the numbers onvthe disclosed disc when the perforated sheets are in their different positions over said numbered discs.

26. A puzzle comprising a board, blocks removably positioned upon the board and numbered upon their, opposite "faces, and cards having openings formed therein for certain 'of the blocks when the cards are placed over the boards, the cards having the same number of openings but no two cards having the openings cut in the same relative arrangement. I

27. A puzzle comprising a playing board, numbered blocks removablyopositioned upon said board, and cards each provided with a plurality of openings disclosing a predetermined number of numbered blocks when the cards are placed over the board, these blocks being so arranged upon the board that the sum of the numbers disclosed through the openings will at all times have the same result.

28. A puzzle comprising a board, a pluralit of blocks removably positioned upon said board and having numbers provided thereon, and a card having a plurality of openings formed therein, the openings being so arranged that added numbers of the blocks showing through the openings will producethe same amount when added, regardless of the the playing board.

29. A puzzle comprising a board having sockets formed therein, blocks fitting into the sockets and removable therefrom and having numbers provided on their upper faces. and acard having openings formed therein for disclosing certain of the blocks when the cards are placed over the board,

the numbers disclosed through the openings adding to produce the same result without regard to positioning the cards when the bloc-ks are properly placed upon the board.

30. A puzzle comprising aboard, blocks positioned upon the board and removable therefrom and having numbers provided upon their upper faces, and cards each havposition of the cards .upon

ing a plurality of openings formed therein forshowingcertain of the blocks through the openings with the numbers disclosed at all times when added producing the same result without regard to the cards selected or the position of the card upon the board when the blocks are properly arranged upon the board.

31. A puzzle comprising a board, blocks removably. positioned upon the board and numbered to correspond to the number of blocks on one face, the, cards having openings formed therein for disclosing certain of the blocks when the cards are placed over the board, the cards having the same ,nu1n-' ber of openings but no two cards having openings cut in the same relative arrangement.

32. A puzzle comprising a board, num

bered .disksarranged on said board so that a predetermined number ofithe disks will produce a predetermined sum when the num forated sheet having the perforations arranged differently and adapted for a number of various positions over said disks.

In testimony whereof I affix my signature of June, 1920.

this 25thday v a WILLIAM MILLER.

'rious positions over said disks, each per- 

